James Arthur (mathematician)

James Arthur
Born (1944-05-18) May 18, 1944
Hamilton, Ontario, Canada
Nationality Canadian
Alma mater University of Toronto
Yale University
Known for Arthur–Selberg trace formula
Arthur conjectures
Awards John L. Synge Award (1987)
CRM-Fields-PIMS prize (1997)
Henry Marshall Tory Medal (1997)
Gerhard Herzberg Canada Gold Medal for Science and Engineering (1999)
Wolf Prize in Mathematics (2015)
Leroy P. Steele Prize for Lifetime Achievement (2017)
Scientific career
Fields Mathematics
Institutions Yale University
Duke University
University of Toronto
Thesis Analysis of Tempered Distributions on Semisimple Lie Groups of Real Rank One (1970)
Doctoral advisor Robert Langlands

James Greig Arthur (born May 18, 1944)[1] is a Canadian mathematician working on harmonic analysis, and former President of the American Mathematical Society. He is currently in the Mathematics Department of the University of Toronto.

Born in Hamilton, Ontario, Arthur received a B.Sc. from the University of Toronto in 1966, and a M.Sc. from the same institution in 1967. He received his Ph.D. from Yale University in 1970. Arthur taught at Yale from 1970 until 1976. He joined the faculty of Duke University in 1976. He has been a professor at the University of Toronto since 1978.[1] He was four times a visiting scholar at the Institute for Advanced Study between 1976 and 2002.[2]

A student of Robert Langlands, he is known for the Arthur–Selberg trace formula, generalizing the Selberg trace formula from the rank-one case (due to Selberg himself) to general reductive groups, one of the most important tools for research on the Langlands program. He also introduced the Arthur conjectures.

Arthur was elected a Fellow of the Royal Society of Canada in 1981 and a Fellow of the Royal Society in 1992.[3][4] He was elected a Foreign Honorary Member of the American Academy of Arts and Sciences in 2003.[5] In 2012 he became a fellow of the American Mathematical Society.[6]


  1. 1 2 "James Greig Arthur". International Mathematical Union. Archived from the original on 15 August 2011. Retrieved 25 April 2011.
  2. Institute for Advanced Study: A Community of Scholars Archived 2013-01-06 at the Wayback Machine.
  3. "Search Fellows". Royal Society of Canada. Retrieved September 7, 2017.
  4. "James Arthur". Royal Society. Retrieved April 3, 2018.
  5. "Book of Members, 1780–2010: Chapter A" (PDF). American Academy of Arts and Sciences. Retrieved 25 April 2011.
  6. "List of Fellows of the American Mathematical Society". Retrieved 3 November 2012.

Further reading

  • Langlands, Robert P. (2001). "The trace formula and its applications: an introduction to the work of James Arthur". Canadian Mathematical Bulletin. 44 (2): 160–209. doi:10.4153/CMB-2001-020-8. ISSN 0008-4395. MR 1827854.
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